Orchids are some of the easiest plants to propagate from cuttings. To do it right you need to know the right place on the stem to cut the orchid. To know the right place you have to know something about the orchid that you're choosing to propagate.
Orchids are either epiphytic, meaning they live up in the trees, or terrestrial, meaning they grow on the ground. If you know what kind of orchid you are growing you can easily find out if it's epiphytic or terrestrial. And remember that no matter what type of orchid you have, that if you're going to cut it, to be sure to use sterile tools. It's also good to use cinnamon, a natural bacteriacide, on the cut ends of the stems. You don't want any pesky diseases to be spread from one orchid to another.
If your orchid is epiphytic, it will probably be sending out aerial roots from one or more places on the stem. Cut the stem just BELOW these roots. Next, put a small amount of potting medium in a pot with good drainage. Hold the stem in the medium with the roots facing down and put in enough medium to cover the roots and to hold the stem in place. Give the new rooting lots of water. However, make sure that your cutting is never sitting in lots of water.
If your orchid is terrestrial, take a cutting from near the base of the orchid and make sure you get at least one pseudobulb and a couple of roots. Put some potting medium in a small pot with at least moderate drainage. Hold the cutting in place with the roots facing down and put some more potting medium on top, again, to hold down the cutting and to cover the roots. Make sure that the pseudobulb or pseudobulbs are above the potting medium.
If done right, the orchid plant that grows from your cutting should bloom in about a year. This is the easy way to grow an orchid from a stem. There is information out that that suggests autoclaving the instruments you use to insure that they're sterile and even scrubbing the cutting with a bleach solution before planting it. Now, I suppose, if you were attempting to propagate an extremely rare or expensive orchid that this would make sense. But for the average orchid hobbyist the process above should work just fine.